Lambda or Not Lambda Arman Shafieloo Korea Astronomy and Space Science Institute 2 nd APCTP-TUS Workshop on Dark energy Tokyo University of Science, August 2-5 2015
Standard Model of Cosmology Using measurements and statistical techniques to place sharp constraints on parameters of the standard cosmological model. Baryon density Initial Conditions: ! b Neutrino mass and Form of the Primordial radiation density: Dark Matter is Cold Spectrum is Power-law fixed by and weakly assumptions and ! dm Interacting : CMB temperature n s , A s Dark Energy is Cosmological Constant : Epoch of reionization ! " = 1 #! b #! dm ! Hubble Parameter and Universe is Flat the Rate of Expansion H 0
Standard Model of Cosmology Using measurements and statistical techniques to place sharp constraints on parameters of the standard cosmological model. Baryon density Initial Conditions: ! b Combination of Assumptions Neutrino mass and Form of the Primordial radiation density: Dark Matter is Cold Spectrum is Power-law assumptions and and weakly CMB temperature ! dm Interacting : n s , A s Dark Energy is Cosmological Constant : Epoch of reionization ! " = 1 #! b #! dm ! Hubble Parameter and Universe is Flat the Rate of Expansion H 0
Why such assumptions? Hints from Cosmological Observations 1991-94 2001-2010 2009-2011 CMBPol/COrE 2020+
Statistics of CMB CMB Anisotropy Sky map => Spherical Harmonic decomposition l ∞ T ( , ) a lm Y ( , ) ∑ ∑ Δ θ φ = θ φ lm l 2 m l = = − * a a C δ δ = lm l m ' ' l ll ' mm ' Gaussian Random field => Completely specified by angular power spectrum l(l+1)C l : Power in fluctuations on angular scales of ~ π /l
Sensitivity of the CMB acoustic temperature spectrum to four fundamental cosmological parameters. Total density Dark Energy Baryon density and Matter density. From Hu & Dodelson, 2002
2015
M. Tegmark et al, 2006 Large Scale Structure Data and Distribution of Galaxies Bassett & Hlozek, 2010
Large Scale Structure Data and Distribution of Galaxies Bassett & Hlozek, 2010
Measuring Distances in Astronomy SNe Ia: Standardized Candles distance-redshift measurements y t i s n e must stretch by a factor of 1.83 t n to match; so SN 1997ap is at a i redshift of 0.83 Very low redshift Sne Ia 10000 15000 5000 wavelength (Angstroms, 10 -10 meters) 10
Universe is Accelerating Universe is not Accelerating ( ) z µ z
Union 2.1 supernovae Ia Compilation
Standard Model of Cosmology combination of reasonable Using measurements and statistical techniques to place sharp constraints on parameters of the standard assumptions, but … .. cosmological model. Baryon density Initial Conditions: ! b Neutrino mass and Form of the Primordial radiation density: Dark Matter is Cold Spectrum is Power-law assumptions and and weakly CMB temperature ! dm Interacting : n s , A s Dark Energy is Cosmological Constant : Epoch of reionization ! " = 1 #! b #! dm ! Hubble Parameter and Universe is Flat the Rate of Expansion H 0
Beyond the Standard Model of Cosmology • The universe might be more complicated than its current standard model (Vanilla Model). • There might be some extensions to the standard model in defining the cosmological quantities. • This needs proper investigation, using advanced statistical methods, high performance computational facilities and high quality observational data.
(Present) t Standard Model of Cosmology Universe is Flat Universe is Isotropic Universe is Homogeneous (large scales) Dark Energy is Lambda (w=-1) Power-Law primordial spectrum (n_s=const) Dark Matter is cold All within framework of FLRW
Era of Accelerating Universe • Mid 90’s: Indirect evidences were seen in the distribution of the galaxies where SCDM could not explain the excess of power at large scales. • 1998: Direct evidence came by Supernovae Type Ia Observations. Going to higher redshifts, supernovae are fainter than expected. One can explain this only (?!=Nobel Prize) by considering an accelerating universe.
Accelerating Universe, Now-2015 Or better to say, ruling out zero-Lambda Universe Hazra, Shafieloo, Souradeep, PRD 2013 Free PPS, No H0 Prior FLAT LCDM Union 2.1 SN Ia Compilation Non FLAT LCDM Power-Law PPS WiggleZ BAO D. Sherwin et.al, PRL 2011
Accelerating Universe, Now Hazra, Shafieloo, Souradeep, PRD 2013 Free PPS, No H0 Prior Something seems to be there, but, FLAT LCDM Union 2.1 SN Ia Compilation What is it? Non FLAT LCDM Power-Law PPS WiggleZ BAO D. Sherwin et.al, PRL 2011
Dark Energy Models • Cosmological Constant • Quintessence and k-essence (scalar fields) • Exotic matter (Chaplygin gas, phantom, etc.) • Braneworlds (higher-dimensional theories) • Modified Gravity • …… But which one is really responsible for the acceleration of the expanding universe?!
Universe is Accelerating There are two models here! Universe is not Accelerating ( ) z µ z
Reconstructing Dark Energy To find cosmological quantities and parameters there are two general approaches: 1. Parametric methods Easy to confront with cosmological observations to put constrains on the parameters, but the results are highly biased by the assumed models and parametric forms. 2. Non Parametric methods Difficult to apply properly on the raw data, but the results will be less biased and more reliable and independent of theoretical models or parametric forms. .
Problems of Dark Energy Parameterizations (model fitting) Brane Model Kink Model Quintessence DE?! Phantom DE?! Shafieloo, Alam, Sahni & Holsclaw et al, PRD 2011 Starobinsky, MNRAS 2006 Chevallier-Polarski-Linder ansatz (CPL). .
Model independent reconstruction of the expansion history Crossing Statistic + Smoothing Gaussian Processes Shafieloo, JCAP (b) 2012 Shafieloo, Kim & Linder, PRD 2012
Dealing with observational uncertainties in matter density (and curvature) • Small uncertainties in the value of matter density affects the reconstruction exercise quiet dramatically. • Uncertainties in matter density is in particular bound to affect the reconstructed w(z). 2 ( 1 z ) H # + ( ) 1 " 1 ! 3 H d d ( z ) ' $ - * $ = H ( z ) L DE H = + ( % " 2 3 1 ( 0 ) ( 1 z ) dz 1 z " ! + + , ) & # 0 M H
erroneous 0.22 Ω = 0 m true 0.27 Ω = 0 m erroneous 0.32 Ω = V. Sahni, A. Shafieloo, A. Starobinsky, 0 m Phys. Rev. D (2008)
Full theoretical picture: Cosmographic Degeneracy
Cosmographic Degeneracy • Cosmographic Degeneracies would make it so hard to pin down the actual model of dark energy even in the near future. 2 ( 1 z ) H + ʹ″ ( ) 1 − 3 H ω = DE H 2 3 1 ( 0 ) ( 1 z ) − Ω + 0 M H Indistinguishable from each other! Shafieloo & Linder, PRD 2011
Reconstruction & Falsification Considering (low) quality of the data and cosmographic degeneracies we should consider a new strategy sidewise to reconstruction: Falsification. Yes-No to a hypothesis is easier than characterizing a phenomena. We should look for special characteristics of the standard model But, How? and relate them to observables .
Falsification of Cosmological Constant • Instead of looking for w(z) and exact properties of dark energy at the current status of data, we can concentrate on a more reasonable problem: Λ OR NOT Λ Yes-No to a hypothesis is easier than characterizing a phenomena
w z = − ( ) 0.7 w z = − ( ) 1.3 2 2 3 H ( ) z H (1 z ) ⎡ ⎤ = Ω + + Ω ⎣ ⎦ 0 0 m DE 1 w z ( ') + ⎫ ⎧ z (1 )exp 3 dz ' Ω = − Ω ∫ ⎨ ⎬ DE 0 m 1 z ' 0 + ⎩ ⎭ V. Sahni, A. Shafieloo, A. Starobinsky, PRD 2008
Falsification: Null Test of Lambda Om diagnostic 2 h ( ) 1 z − Om z ( ) = We Only Need h(z) 3 (1 z ) 1 + − Om(z) is constant only V. Sahni, A. Shafieloo, A. Starobinsky, for FLAT LCDM model PRD 2008 Phantom w 1 Om z ( ) = − → = Ω w= -1.1 0 m w 1 Om z ( ) < − → < Ω 0 m Quintessence w 1 Om z ( ) > − → > Ω om w= -0.9
Om diagnostic is very well established SDSS III / BOSS collaboration L. Samushia et al, MNRAS 2013 WiggleZ collaboration C. Blake et al, MNRAS 2011 (Alcock-Paczynski measurement)
Om3 A null diagnostic customized for reconstructing the properties of dark energy directly from BAO data H 2 ( z 2 ) 2 H 0 ! 1 h 2 ( z 2 ) H 2 ( z 2 ) H 2 ( z 2 ) h 2 ( z 1 ) ! 1 H 2 ( z 1 ) ! 1 h 2 ( z 2 ) ! h 2 ( z 1 ) 2 H 0 (1 + z 2 ) 3 ! (1 + z 1 ) 3 (1 + z 2 ) 3 ! (1 + z 1 ) 3 (1 + z 2 ) 3 ! (1 + z 1 ) 3 (1 + z 2 ) 3 ! (1 + z 1 ) 3 Om 3( z 1 , z 2 , z 3 ) = Om ( z 2 , z 1 ) Om ( z 3 , z 1 ) = = = = h 2 ( z 3 ) ! h 2 ( z 1 ) h 2 ( z 3 ) H 2 ( z 2 ) H 2 ( z 3 ) h 2 ( z 1 ) ! 1 H 2 ( z 1 ) ! 1 (1 + z 3 ) 3 ! (1 + z 1 ) 3 2 H 0 ! 1 (1 + z 3 ) 3 ! (1 + z 1 ) 3 (1 + z 3 ) 3 ! (1 + z 1 ) 3 H 2 ( z 2 ) 2 H 0 (1 + z 3 ) 3 ! (1 + z 1 ) 3 Observables Shafieloo, Sahni, Starobinsky, PRD 2013
Characteristics of Om3 Om is constant only for Flat LCDM model Om3 is equal to one for Flat LCDM model Om3 is independent of H0 and the distance to the last scattering surface and can be derived directly using BAO observables. Shafieloo, Sahni, Starobinsky, PRD 2013
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